A kinetic model for chemical reactions without barriers: transport coefficients and eigenmodes

Abstract

The kinetic model of the Boltzmann equation proposed in the work [1] for a binary mixture undergoing chemical reactions of symmetric type which occur without activation energy is revisited here, with the aim of investigating in detail the transport properties of the reactive mixture and the influence of the reaction process on the transport coefficients. Accordingly, the non-equilibrium solution of the Boltzmann equation is determined through an expansion in Sonine polynomials up to the first order, using the Chapman-Enskog method, in a chemical regime for which the reaction process is close to its final equilibrium state. The non-equilibrium deviations are explicitly calculated for what concerns the thermal-diffusion ratio and coefficients of shear viscosity, diffusion and thermal conductivity. The theoretical and formal analysis developed in the present paper is complemented with some numerical simulations performed for different concentrations of reactants and products of the reaction as well as for both exothermic and endothermic chemical processes. The results reveal that chemical reactions without energy barrier can induce an appreciable influence on the transport properties of the mixture. Oppositely to the case of reactions with activation energy, the coefficients of shear viscosity and thermal conductivity become larger than those of an inert mixture when the reactions are exothermic. An application of the non-barrier model and its detailed transport picture is included in this paper, in order to investigate the dynamics of the local perturbations on the constituent number densities, and velocity and temperature of the whole mixture, induced by spontaneous internal fluctuations. It is shown that for the longitudinal disturbances there exist two hydrodynamic sound modes, one purely diffusive hydrodynamic mode and one kinetic mode.

Modeling and analysis of time-dependent processes in a chemically reactive mixture

“…The problem of sound waves corresponds to the propagation of forced waves, and consists in assuming a given real angular frequency ω and solving the dispersion relation (24) for a complex wavenumber κ as function of the oscillation frequency, that is κ = κ(ω). Then, the phase velocity and the attenuation coefficient of the waves can be computed from the roots of the dispersion relation, following a rather standard procedure (see, for example, [7,10,11,12,13,14,15]).…”

“…The oscillation frequency and the oscillation time decay of the disturbances can be computed from the roots of the dispersion relation, following a rather well known procedure (see, for example, Refs. [7,17,18]).…”

“…See Refs. [7,17] for other details on the topic. The solutions also allow us to recognize the effects of the chemical reaction on the spectrum.…”

“…Among others, we quote here Refs. [1,4,5,6,7,8]. However, in our opinion, other contributions at the level of theoretical and modelling approaches should be of interest in order to deeply investigate the effects of the chemical kinetics on sound propagation within reactive systems.…”

Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions

“…To determine the forward and reverse reaction rate coefficients, we insert each distribution function (32) in the corresponding definition, in Eq. (13).…”